write the simplest polynomial function with the given zeros. 5, -3i

Answer 1

To find to polynomial from zeros.

1. Find the factors. If it is a positive zero, the factor will be (x- zero) If it is a negative zero if is (x+zero)
2. Multiply the factors together.

Zeros of 5 and -3i would be:

1. Find the factors: (x-5)(x+3i)(x-3i) When you have one complex zero, it has to have a pair. The other one is the complex conjugate, same value different sign.
2. Multiply the factors together: Will start out with FOIL for (x+3i)(x-3i) = x²+3ix-3ix-9i² = x²+9

Then multiply by the last factor

(x-5)(x²+9) n

Now FOIL these

x³-5x²+9x-45